Question

Iron is extracted from its ore via the reaction
$Fe_2O_3, + 3 CO→ 2 Fe + 3CO_2$
The volume of CO (at STP) required to produce 1 kg of iron is ________liters. (round off to the nearest integer)
[Given: Atomic wt. of Fe = 56; assume STP to be 0 °C and 1 atm]

Answer 1

Correct Answer: 599

To find the volume of CO needed at STP to produce 1 kg of iron, follow these steps:
1. **Determine Moles of Iron Produced:**
The atomic weight of Fe is given as 56 g/mol. So, for 1 kg (1000 g) of Fe, the moles of Fe are:
\( \text{Moles of Fe} = \frac{1000}{56} \approx 17.857 \text{ mol} \)
2. **Relate Moles of Fe to CO:**
The balanced chemical equation is:
\( Fe_2O_3 + 3CO \rightarrow 2Fe + 3CO_2 \)
From the equation, 2 moles of Fe are produced for every 3 moles of CO. Therefore, moles of CO required are:
\( \text{Moles of CO} = \frac{3}{2} \times 17.857 \approx 26.786 \text{ mol} \)
3. **Calculate Volume of CO at STP:**
At STP (Standard Temperature and Pressure), 1 mole of any ideal gas occupies 22.4 liters. Thus, volume of CO is:
\( \text{Volume of CO} = 26.786 \times 22.4 \approx 599 \text{ liters} \)
Final Answer: The volume of CO required is 599 liters.